The University of Edinburgh -
Division of Informatics
Forrest Hill & 80 South Bridge

PhD Thesis #9207

Title:Aspects of the Constructive Omega Rule Within Automated Deduction
Date: 1992
Abstract:In general, cut elimination holds for arithmetical systems with the omega-rule, but not for systems with ordinary induction. Hence in the latter, there is the problem of generalisation, since arbitrary formulae can be cut in. This makes automatic theorem-proving very difficult. An important technique for investigating derivability in formal systems of arithmetic has been to embed such systems into semi-formal systems with the omega-rule. This thesis describes the implementation of such a system. Moreover, an important application is presented in the form of a new method of generalisation by means of "guiding proofs" in the stronger system, which sometimes succeeds in producing proofs in the original system when other methods fail.

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